You are looking to start a catering business. Part of the business is figuring out who should be used to transport prepared food to different locations

Question

You are looking to start a catering business. Part of the business is figuring out who should be used to transport prepared food to different locations. You have found two trucking companies that are willing to make sure the food arrives intact. Peter’s Pick Up charges a flat fee of $68 for each job plus $0.40 per mile. Helen’s Haulers charges a flat fee of $23 for each job plus $0.65 per mile. Write an algebraic explanation that explains the total cost of Helen's Haulers, then figure out when Peter's pickup would be cheaper than Helens haulers. Finally, 4. Write a function equation that describes how to find the total cost (y) given the number of miles (x) for both Peter’s Pick Up and Helen’s Haulers. Write the function in y=mx+b form

Answer 1

It appears that this problem requires the algebraic equations for each company's total cost, and then a comparison of the two. Each equation can be written in the form of a line, y = mx+b. y is the total cost, and x is the number of miles traveled.

 

Peter's Pickup

y = 0.40*x + 68

 

Helen's Haulers

y = 0.65*x + 23

 

To determine when Peter's Pickup will become cheaper than Helen's Haulers, we must set the equations equal to eachother:

 

0.40*x+68 = 0.65*x+23

 

Solving:

 

0.40*x+45 = 0.65*x

45 = 0.25*x

45/0.25 = x

 

x = 180 miles

 

Therefore, Peter's Pickup will have the same total cost as Helen's Haulers after driving 180 miles. This means that Peter's Pickup will be cheaper for driving distances greater than 180 miles, and Helen's Haulers will be cheaper for driving distances less than 180 miles.